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Recent Results in Nonlinear Elliptic Equations and their Interactions with Geometry October 31, 2005 - November 04, 2005
Registration Deadline: September 25, 2005 over 13 years ago
To apply for Funding you must register by: July 31, 2005 over 13 years ago
Parent Program: --
Organizers Frank Pacard, Neil Trudinger and Paul Yang

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This workshop will focus on recent developments in nonlinear elliptic equations and their interactions with differential geometry, Riemannian geometry and complex geometry. Topics will include the study of fully nonlinear elliptic problems which arise for example in the study of hessian equations for hypersurfaces, in complex Kahler geometry or in the prescription of the k-th symmetric functions of the eigenvalues of the Schouten tensor in conformal geometry and its analogue in CR geometry. It will also include the analysis of higher order elliptic equations which arise in affine geometry and conformal geometry. Lecture Schedule with Talk Abstracts SCHEDULE Monday, October 31 9:30 – 10:30 Gang Tian (Princeton Univ.), "Curvature estimate for 4-dimensional Einstein equation" 10:30 – 11:00 Morning Tea – Sixth Floor 11:00 – 12:00 Xiuxiong Chen (Univ. of Wisconsin), "On the Calabi functional in Kahler manifold" 12:00 – 1:00 Jeff Viaclovsky (MIT), “Volume Growth, Curvature Decay, and Critical Metrics” 1:00 – 2:30 Lunch 2:30 – 3:30 Xavier Cabre (ICREA-Univ. Politecnica Catalunya), "Regularity of radial minimizers and extremal radial solutions of semilinear elliptic equations" 3:30 – 4:00 Travel to 60 Evans Hall, UCB 4:10 – 5:10 (At 60 Evans Hall, UCB) Cristian Gutierrez (Temple University), “The Monge-Ampere equation: Overview and Recent Results” Tuesday, November 1 9:30 – 10:30 Richard Schoen (Stanford University), "Blowup issues for the Yamabe equation on high dimensional manifolds" 10:30 – 11:00 Morning Tea – Sixth Floor 11:00 – 12:00 Simon Brendle (Stanford University), "Global convergence of the Yamabe flow in dimension 6 and higher" 12:00 – 1:00 Olivier Druet (ENS Lyons), “The prescribed scalar curvature problem” 1:00 – 2:30 Lunch 2:30 – 3:30 Bernd Amman (Univ. Nancy), "The first Dirac eigenvalue in a conformal class" 3:30 – 4:00 Afternoon Tea – Sixth Floor 4:00 – 5:00 Xiaohua Zhu (Beijing University), “Kahler-Ricci flow and certain complex Monge-Ampere equation" Wednesday, November 2 9:30 – 10:30 Gerhard Huisken (Max Planck Inst. f. Gravitationsphysik), "Rigidity inequalities via inverse mean curvature flow" 10:30 – 11:00 Morning Tea – Sixth Floor 11:00 – 12:00 J. Cheng (Academica Sinica, Taipei), "The mean curvature equation in Pseudohermitian geometry" 12:00 – 1:00 Sophie Chen (Princeton University), “Boundary Estimates for Some Fully Nonlinear PDEs and Applications to Conformal Geometry” 1:00 – 2:30 Lunch 2:30 – 3:30 Qing Han (Univ. of Notre Dame), “Smooth local isometric embedding of surfaces with Gauss curvature changing sign monotonically across a curve” 3:30 – 4:00 Afternoon Tea – Sixth Floor 4:00 – 5:00 Nassif Ghoussoub (Univ. of British Columbia), "Selfdual variational principles for PDEs and evolution equations" Thursday, November 3 9:30 – 10:30 Bruno Franchi (Univ. of Bologna), "Intrinsic submanifolds of Heisenberg group" 10:30 – 11:00 Morning Tea – Sixth Floor 11:00 – 12:00 Joel Spruck (Johns Hopkins Univ.), "Complete hypersurfaces of constant curvature in Hyperbolic space with prescribed asymptotic boundary" 12:00 – 1:00 Refe Mazzeo (Stanford University), “Einstein metrics and higher rank geometry” 1:00 – 2:30 Lunch 2:30 – 3:30 Brian White (Stanford University), "Getting a handle on the helicoid" 3:30 – 4:00 Afternoon Tea – Sixth Floor 4:00 – 5:00 Xujia Wang (Australian National Univ.), “Fully nonlinear partial differential equations and applications in geometry” Friday, November 4 9:30 – 10:30 Luis Caffarelli (Univ. of Texas, Austin), "On homogenization and rates of convergence for random fully nonlinear equations" 10:30 – 11:00 Morning Tea – Sixth Floor 11:00 – 12:00 Alice Chang (Princeton Univ.), "Conformal invariants associated with a smooth measure" 12:00 – 1:00 Rod Gover (Univ. of Auckland) “Conformal Laplacian operators and Q-curvature on Einstein manifolds” 1:00 – 2:30 Lunch 2:30 – 3:30 Jie Qing (UC Santa Cruz), "“On semi-linear conformally invariant PDE” 3:30 – 4:00 Afternoon Tea – Sixth Floor 4:00 – 5:00 Fengbo Hang (Princeton & Michigan State Univ.), “On the higher order Q curvature on the Sphere”
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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To apply for funding, you must register by the funding application deadline displayed above.

Students, recent Ph.D.'s, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

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A block of rooms has been reserved at the Hotel Durant. Reservations may be made by calling 1-800-238-7268. When making reservations, guests must request the MSRI preferred rate. If you are making your reservations on line, please go to this link and enter the promo/corporate code MSRI123. Our preferred rate is $129 per night for a Deluxe Queen/King, based on availability.

Additional lodging options (short term housing page - Short Term Housing

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Schedule, Notes/Handouts & Videos
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Oct 31, 2005
09:30 AM - 10:30 AM
  Curvature Estimate for 4-dimensional Einstein Equation.
Gang Tian (Princeton University)
11:00 AM - 12:00 PM
  On the Calabi Functional in Kahler Manifold
Xiu-Xiong Chen
12:00 PM - 01:00 PM
  Volume Growth, Curvature Decay, and Critical Metrics
Jeff Viaclovsky (University of Wisconsin-Madison)
02:30 PM - 03:30 PM
  Regularity of Radial Minimizers and Extremal Radial Solutions of Semilinear Elliptic Equations.
Xavier Cabré (Polytechnical University of Cataluña (Barcelona))
Nov 01, 2005
09:30 AM - 10:30 AM
  Blowup Issues for the Yamabe Equation on High Dimensional Manifolds.
Richard Schoen (University of California, Irvine)
11:00 AM - 12:00 PM
  Global Convergence of the Yamabe Flow in Dimension 6 and Higher.
Simon Brendle (Stanford University)
12:00 PM - 01:00 PM
  The Prescribed Scalar Curvature Problem.
Olivier Druet
02:30 PM - 03:30 PM
  The First Dirac Eigenvalue in a Conformal Class.
Bernd Ammann (Universität Regensburg)
04:00 PM - 05:00 PM
  Kahler-Ricci Flow and Certain Complex Monge-Ampere Equation.
Xiaohua Zhu (Peking University)
Nov 02, 2005
09:30 AM - 10:30 AM
  Rigidity Inequalities Via Inverse Mean Curvature Flow.
Gerhard Huisken (Math. Forschungsinstitut Oberwolfach)
11:00 AM - 12:00 PM
  The Mean Curvature Equation in Pseudohermitian Geometry.
Jih-Hsin Cheng
12:00 PM - 01:00 PM
  Boundary Estimates for Some Fully Nonlinear PDEs and Applications to Conformal Geometry.
Szu-yu Sophie Chen
02:30 PM - 03:30 PM
  Smooth Local Isometric Embedding of Surfaces with Gauss Curvature Changing Sign Monotonically Across a Curve.
Qing Han
04:00 PM - 05:00 PM
  Selfdual Variational Principles for PDEs and Evolution Equations.
Nassif Ghoussoub (University of British Columbia)
Nov 03, 2005
09:30 AM - 10:30 AM
  On Semi-linear Conformally Invariant PDE.
Jie Qing (University of California, Santa Cruz)
11:00 AM - 12:00 PM
  Complete Hypersurfaces of Constant Curvature in Hyperbolic Space with Prescribed Asymptotic Boundary.
Joel Spruck (Johns Hopkins University)
12:00 PM - 01:00 PM
  Einstein Metrics and Higher Rank Geometry.
Rafe Mazzeo (Stanford University)
02:30 PM - 03:30 PM
  Getting a Handle on the Helicord.
Brian White (Stanford University)
04:00 PM - 05:00 PM
  Fully Nonlinear Partial Differential Equations and Applications in Geometry.
Xu-Jia Wang (Australian National University)
Nov 04, 2005
11:00 AM - 12:00 PM
  Conformal Invariants Associated with a Smooth Measure.
Sun-Yung Chang (Princeton University)
12:00 PM - 01:00 PM
  Conformal Laplacian Operators and Q-curvature on Einstein Manifolds.
Ashwin Gover
02:30 PM - 03:30 PM
  Intrinsic Submanifolds of Heisenberg Group.
Bruno Franchi
04:00 PM - 05:00 PM
  On the Higher Order Q Curvature on the Sphere.
Fengbo Hang